toms923

toms923, a MATLAB code which evaluates the Pfaffian for a dense or banded skew symmetric matrix, by Michael Wimmer.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

toms923 is available in a MATLAB version and a Python version.

Related Data and Programs:

toms923_test

test_matrix, a MATLAB code which defines test matrices for which the condition, determinant, eigenvalues, inverse, null vectors, P*L*U factorization or linear system solution are already known, including the Vandermonde and Wathen matrix.

Reference:

1. Michael Wimmer,
   Algorithm 923: Efficient Numerical Computation of the Pfaffian for Dense and Banded Skew-Symmetric Matrices,
   ACM Transactions on Mathematical Software,
   Volume 38, Number 4, Article 30, August 2012.

Source Code:

• pfaffian_hessenberg.m, computes the Pfaffian of a real skew-symmetric matrix. Based on the real Hessenberg decomposition.
• pfaffian_householder.m, computes the Pfaffian of a skew-symmetric matrix. Based on the Householder tridiagonalization.
• pfaffian_LTL.m, computes the Pfaffian of a skew-symmetric matrix. Based on the Parlett-Reid algorithm.
• skew_LTL.m, computes the LTL^T decomposition of a skew-symmetric matrix using the Parlett-Reid algorithm.
• skew_tridiagonalize.m, computes the tridiagonal form of a skew-symmetric matrix under unitary congruence (Householder tridiagonalization).